The Collison brothers—Patrick and John—started Stripe in 2010 after dropping out of college (MIT and Harvard, respectively) several years earlier. The premise: Create an online- and mobile-payments company built from the ground up for the Internet age. Coming from a tech perspective, the brothers believe the challenges companies face in using online payment systems are rooted in code and design—not finance. They set out to build a developer-focused, instant setup payment platform that any company could use and scale to size.

Some heavy hitters believed in their vision. Three of PayPal's founders (Peter Thiel, Max Levchin and Elon Musk), as well as Sequoia Capital, were early investors. Since its start several years ago, the San Francisco-based company is processing billions of dollars' worth of transactions for thousands of companies, including such tech darlings as Foursquare and Lyft, as well as retailing behemoth Wal-Mart.

True, the company does daily battle against industry stalwart PayPal, but few are betting that the Collison brothers won't give that company a run for its money.

How did you come up with your big idea?

"While it has become easier to build and launch an online business on almost every front, payments processing has remained dominated by clunky legacy players. ... So we built Stripe."-John Collison, co-founder and CEO